To name a few: safety enforced at compile-time without any sort of GC/ARC (probably the biggest), more precise control over the hardware (e.g. more concrete pointers), the lack of a required runtime -- basically it has much better support for low-level features while not sacrificing many high-level features.
I believe tptacek was asking for the intersection of features between Swift and Rust, not for features that Rust has but Swift doesn't (like compile-time memory safety without GC/ARC).
Protocols being used both as type parameter constraints and as types themselves reminded a few people of Rust's traits, but of course Rust didn't come up with those from whole cloth either.
The biggest thing I see is that it's an imperative language with functional-style ADT's, tuples, sum types, etc.
It also looks fairly similar syntactically (all those let's).
Not sure if there are other things it has in common.